{
 "metadata": {
  "name": "",
  "signature": "sha256:6c749088d705afea551d660843d43712294b403eb88b554a30416fb4f6ab61c7"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Zhenfeng Liang"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# MTH9879 Homework 4\n",
      "\n",
      "Assigned: February 24, 2015.\n",
      "Due: March 10, 2015 by 6pm. \n",
      "\n",
      "Late homework **will not be accepted**.\n",
      "\n",
      "$$\n",
      "\\newcommand{\\supp}{\\mathrm{supp}}\n",
      "\\newcommand{\\E}{\\mathbb{E}}\n",
      "\\newcommand{\\Eof}[1]{\\mathbb{E}\\left[ #1 \\right]}\n",
      "\\def\\Cov{{ \\mbox{Cov} }}\n",
      "\\def\\Var{{ \\mbox{Var} }}\n",
      "\\newcommand{\\1}{\\mathbf{1} }\n",
      "\\newcommand{\\PP}{\\mathbb{P} }\n",
      "%\\newcommand{\\Pr}{\\mathrm{Pr} }\n",
      "\\newcommand{\\QQ}{\\mathbb{Q} }\n",
      "\\newcommand{\\RR}{\\mathbb{R} }\n",
      "\\newcommand{\\DD}{\\mathbb{D} }\n",
      "\\newcommand{\\HH}{\\mathbb{H} }\n",
      "\\newcommand{\\spn}{\\mathrm{span} }\n",
      "\\newcommand{\\cov}{\\mathrm{cov} }\n",
      "\\newcommand{\\sgn}{\\mathrm{sgn} }\n",
      "\\newcommand{\\HS}{\\mathcal{L}_{\\mathrm{HS}} }\n",
      "%\\newcommand{\\HS}{\\mathrm{HS} }\n",
      "\\newcommand{\\trace}{\\mathrm{trace} }\n",
      "\\newcommand{\\LL}{\\mathcal{L} }\n",
      "%\\newcommand{\\LL}{\\mathrm{L} }\n",
      "\\newcommand{\\s}{\\mathcal{S} }\n",
      "\\newcommand{\\ee}{\\mathcal{E} }\n",
      "\\newcommand{\\ff}{\\mathcal{F} }\n",
      "\\newcommand{\\hh}{\\mathcal{H} }\n",
      "\\newcommand{\\bb}{\\mathcal{B} }\n",
      "\\newcommand{\\dd}{\\mathcal{D} }\n",
      "\\newcommand{\\g}{\\mathcal{G} }\n",
      "\\newcommand{\\p}{\\partial}\n",
      "\\newcommand{\\half}{\\frac{1}{2} }\n",
      "\\newcommand{\\T}{\\mathcal{T} }\n",
      "\\newcommand{\\bi}{\\begin{itemize}}\n",
      "\\newcommand{\\ei}{\\end{itemize}}\n",
      "\\newcommand{\\beq}{\\begin{equation}}\n",
      "\\newcommand{\\eeq}{\\end{equation}}\n",
      "\\newcommand{\\beas}{\\begin{eqnarray*}}\n",
      "\\newcommand{\\eeas}{\\end{eqnarray*}}\n",
      "\\newcommand{\\cO}{\\mathcal{O}}\n",
      "\\newcommand{\\cF}{\\mathcal{F}}\n",
      "\\newcommand{\\cL}{\\mathcal{L}}\n",
      "\\newcommand{\\BS}{\\text{BS}}\n",
      "$$\n",
      "\n",
      "$$\n",
      "\\newcommand{\\bea}{\\begin{eqnarray}}\n",
      "\\newcommand{\\eea}{\\end{eqnarray}}\n",
      "\\newcommand{\\supp}{\\mathrm{supp}}\n",
      "\\newcommand{\\F}{\\mathcal{F} }\n",
      "\\newcommand{\\cF}{\\mathcal{F} }\n",
      "\\newcommand{\\E}{\\mathbb{E} }\n",
      "\\newcommand{\\Eof}[1]{\\mathbb{E}\\left[ #1 \\right]}\n",
      "\\def\\Cov{{ \\mbox{Cov} }}\n",
      "\\def\\Var{{ \\mbox{Var} }}\n",
      "\\newcommand{\\1}{\\mathbf{1} }\n",
      "\\newcommand{\\p}{\\partial}\n",
      "\\newcommand{\\PP}{\\mathbb{P} }\n",
      "\\newcommand{\\Pof}[1]{\\mathbb{P}\\left[ #1 \\right]}\n",
      "\\newcommand{\\QQ}{\\mathbb{Q} }\n",
      "\\newcommand{\\R}{\\mathbb{R} }\n",
      "\\newcommand{\\DD}{\\mathbb{D} }\n",
      "\\newcommand{\\HH}{\\mathbb{H} }\n",
      "\\newcommand{\\spn}{\\mathrm{span} }\n",
      "\\newcommand{\\cov}{\\mathrm{cov} }\n",
      "\\newcommand{\\HS}{\\mathcal{L}_{\\mathrm{HS}} }\n",
      "\\newcommand{\\Hess}{\\mathrm{Hess} }\n",
      "\\newcommand{\\trace}{\\mathrm{trace} }\n",
      "\\newcommand{\\LL}{\\mathcal{L} }\n",
      "\\newcommand{\\s}{\\mathcal{S} }\n",
      "\\newcommand{\\ee}{\\mathcal{E} }\n",
      "\\newcommand{\\ff}{\\mathcal{F} }\n",
      "\\newcommand{\\hh}{\\mathcal{H} }\n",
      "\\newcommand{\\bb}{\\mathcal{B} }\n",
      "\\newcommand{\\dd}{\\mathcal{D} }\n",
      "\\newcommand{\\g}{\\mathcal{G} }\n",
      "\\newcommand{\\half}{\\frac{1}{2} }\n",
      "\\newcommand{\\T}{\\mathcal{T} }\n",
      "\\newcommand{\\bit}{\\begin{itemize}}\n",
      "\\newcommand{\\eit}{\\end{itemize}}\n",
      "\\newcommand{\\beq}{\\begin{equation}}\n",
      "\\newcommand{\\eeq}{\\end{equation}}\n",
      "\\newcommand{\\tr}{\\mbox{tr}}\n",
      "\\newcommand{\\underbar}{\\underline}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font color = \"red\">Homework is to be done by each student individually.  To receive full credit, you must email a completed copy of this iPython notebook to Yu Gan (yugan323@gmail.com), Fubo Shi (fubo.shi.baruch@gmail.com), and Tai-Ho Wang (tai-ho.wang@baruch.cuny.edu) by the due date and time.  All R-code must run correctly and solutions must be written up neatly in Markdown/LaTeX format.\n",
      "\n",
      "<font color=\"blue\">If you encounter problems with Markdown/LaTeX or iPython notebook, please contact your TAs Yu Gan and/or Fubo Shi.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 0. (0 points) \n",
      "Read Chapter 5 and 6 of Hasbrouck and Chapters 2 and 3 of Foucault, Pagano and R&ouml;ell. \n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Glosten and Milgrom"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 1. (8 points) \n",
      "\n",
      "(Adapted from Hasbrouck 5.2 but please note that the setup in (3) in the slides is different from Hasbrouck's in Figure 5.1 of his book.) Consider a variant of the Glosten and Milgrom model where there is informed trading only in the low state $V=\\underline V$.\n",
      "\n",
      "(a) Show that the learned probability after one step that the true price is $\\bar V$ is given by\n",
      "\n",
      "$$\n",
      "\\delta_1(Buy)=\\Pr(\\bar V|Buy)=\\frac{\\delta}{1-\\mu\\,(1-\\delta)};\\quad \\delta_1(Sell)=\\Pr(\\bar V|Sell)=\\frac{\\delta}{1+\\mu\\,(1-\\delta)}\n",
      "$$\n",
      "\n",
      "and that\n",
      "\n",
      "$$\n",
      "A=\\frac{\\underline V\\,{(1-\\delta)\\,(1-\\mu)}+\\bar V\\,{\\delta}}{{1-\\mu\\,(1-\\delta)}};\\quad B=\\frac{\\underline V\\,{(1-\\delta)\\,(1+\\mu)}+\\bar V\\,{\\delta}}{1+\\mu\\,(1-\\delta)}\n",
      "$$\n",
      "\n",
      "(b) Deduce an expression for the spread $s=A-B$.\n",
      "\n",
      "(c) Explain the sensitivities of the spread to the parameters of the model to a non-expert.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Solution:\n",
      "\n",
      "### (a)\n",
      "For buy,\n",
      "\\begin{eqnarray*}\n",
      "\\Pr(\\bar V \\cap Buy) &=& 0.5 \\delta \\\\\n",
      "\\Pr(\\underbar V \\cap Buy) &=& 0.5(1 - \\delta)(1 - \\mu) \\\\\n",
      "\\end{eqnarray*}\n",
      "\n",
      "$$\n",
      "\\Pr(Buy) = \\Pr(\\bar V \\cap Buy) + \\Pr(\\underbar V \\cap Buy) = 0.5(1 - \\mu (1 - \\delta)) \n",
      "$$\n",
      "So,\n",
      "$$\n",
      "\\delta_1(Buy)=\\Pr(\\bar V|Buy)=\\frac{\\delta}{1-\\mu\\,(1-\\delta)}\n",
      "$$\n",
      "\n",
      "\\begin{eqnarray*}\n",
      "A&=&\\mathbb{E} [V|Buy]\\\\\n",
      "&=& {\\bar V\\,\\Pr(\\bar V|Buy)+\\underbar V\\,\\Pr(\\underbar V|Buy)}\\\\\n",
      "&=& \\frac{\\bar V\\,\\Pr(\\bar V \\cap Buy)+\\underbar V\\,\\Pr(\\underbar V \\cap Buy)}{\\Pr(Buy)} \\\\\n",
      "&=& \\frac{\\underline V\\,{(1-\\delta)\\,(1-\\mu)}+\\bar V\\,{\\delta}}{{1-\\mu\\,(1-\\delta)}}\n",
      "\\end{eqnarray*}\n",
      "\n",
      "For sell,\n",
      "\\begin{eqnarray*}\n",
      "\\Pr(\\bar V \\cap Sell) &=& 0.5 \\delta \\\\\n",
      "\\Pr(\\underbar V \\cap Sell) &=& 0.5(1 - \\delta)(1 + \\mu) \\\\\n",
      "\\end{eqnarray*}\n",
      "\n",
      "$$\n",
      "\\Pr(Sell) = \\Pr(\\bar V \\cap Sell) + \\Pr(\\underbar V \\cap Sell) = 0.5(1 + \\mu (1 - \\delta)) \n",
      "$$\n",
      "\n",
      "$$\n",
      "\\delta_1(Sell)=\\Pr(\\bar V|Sell)=\\frac{\\delta}{1+\\mu\\,(1-\\delta)}\n",
      "$$\n",
      "\n",
      "\\begin{eqnarray*}\n",
      "B&=&\\mathbb{E} [V|Sell]\\\\\n",
      "&=& {\\bar V\\,\\Pr(\\bar V|Sell)+\\underbar V\\,\\Pr(\\underbar V|Sell)}\\\\\n",
      "&=& \\frac{\\bar V\\,\\Pr(\\bar V \\cap Sell)+\\underbar V\\,\\Pr(\\underbar V \\cap Sell)}{\\Pr(Sell)} \\\\\n",
      "&=& \\frac{\\underline V\\,{(1-\\delta)\\,(1 + \\mu)}+\\bar V\\,{\\delta}}{{1 + \\mu\\,(1-\\delta)}}\n",
      "\\end{eqnarray*}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### (b)\n",
      "With some calculation,\n",
      "$$\n",
      "s = A - B = \\frac{2 \\mu \\delta (1 - \\delta)(\\bar V - \\underbar V)}{1 - \\mu^2 (1 - \\delta)^2}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### (c)\n",
      "When the $ \\bar V - \\underbar V$ goes up, the spread between two market states goes up, the market maker have to expand its bid-ask spread, otherwise, there would be arbitrage opportunity for traders.\n",
      "\n",
      "When $\\mu $ goes up, the percentage of the informed traders in the lower marktet state goes up, the market maker have to decrease its bid price to $\\underbar V$, otherwise, there would be arbitrage opportunity for traders.\n",
      "\n",
      "When $\\delta = 0.5$, we have the largest uncertanty of the market, and we have the largest spread."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Set up R environment for the next questions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext rmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "download.file(url=\"http://mfe.baruch.cuny.edu/wp-content/uploads/2015/02/tq.zip\", destfile=\"tq.zip\")\n",
      "unzip(zipfile=\"tq.zip\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "trying URL 'http://mfe.baruch.cuny.edu/wp-content/uploads/2015/02/tq.zip'\n",
        "Content type 'application/zip' length 695952 bytes (679 Kb)\n",
        "opened URL\n",
        "==================================================\n",
        "downloaded 679 Kb\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "library(xts)\n",
      "library(highfrequency)\n",
      "library(quantmod)\n",
      "\n",
      "load(\"tq.rData\")\n",
      "tqdata <- tqBAC"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Lee and Ready tick test"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 2. (10 points) \n",
      "\n",
      "In the following use the trades and quotes object *tqBAC* in the loaded data *tq.rData*.  Denote trade prices by $p_t$ and mid-quotes by $m_t$.\n",
      "\n",
      "(a) Compute the time series of trade signs $\\epsilon_t$ according to $\\epsilon_t=+1$ if $p_t>m_t$ and  $\\epsilon_t=-1$ otherwise, using the Lee-Ready rule for trades at mid.  Name this series *tradeSigns*. (Note this was already done in the lecture.)\n",
      "\n",
      "(b) Compute the Lee-Ready trade-sign indicator time series (as if you didn't have quotes and so no mid-prices).\n",
      "\n",
      "(c) Compute the correlation of these two indicators.\n",
      "\n",
      "(d) Assume the rule in part (a) is 100% accurate.  What percentage of trades are correctly signed by the Lee-Ready test?\n",
      "\n",
      "(e) Explain the relationship between your answers in (c) and (d).\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Functions for question 2\n",
      "\n",
      "LeeReadyTradeSign <- function(){ # Calculate the trade signs according to the Lee-Ready test\n",
      "    p <- as.numeric(tqdata$PRICE)\n",
      "    dp <- diff(p)\n",
      "\n",
      "    result <- rep(0, length(dp) + 1)\n",
      "    # The first deal is buy by default\n",
      "    result[1] = 1\n",
      "    for (i in 1 : length(dp)){\n",
      "        if(dp[i] > 0)\n",
      "            result[i + 1] <- 1\n",
      "        else if(dp[i] < 0)\n",
      "            result[i + 1] <- -1\n",
      "        else if (dp[i] == 0){\n",
      "            result[i + 1] <- result[i]\n",
      "        }\n",
      "    }  \n",
      "    return (result);\n",
      "}\n",
      "            \n",
      "accuratePercent <- function(normalTradeSigns, leeTradeSigns){ # Return the accurate percentage between two signs\n",
      "    count <- 0\n",
      "    len <- length(tradeSigns)\n",
      "    for(i in 1:len){\n",
      "        if(normalTradeSigns[i] == leeTradeSigns[i])\n",
      "            count = count + 1\n",
      "    }\n",
      "    return (count/len)\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Part (a)\n",
      "# Compute trade signs\n",
      "tradeSigns <- getTradeDirection(tqdata) \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Part (b)\n",
      "leeTradeSigns <- LeeReadyTradeSign()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Part (c)\n",
      "cor(tradeSigns, leeTradeSigns)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] 0.661735\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Part (d)\n",
      "percent <- accuratePercent(tradeSigns, leeTradeSigns)\n",
      "percent"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] 0.8296562\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### (e)\n",
      "The part (d) shows that there is high percentage, 82.97%, of trades are correctly signed by Lee-Ready test which is consistent with part (c), a high correlation."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Realized spread by exchange"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 3. (8 points)\n",
      "\n",
      "(a) Reproduce Figure 6 from the lecture slides, making sure to get the aesthetics right.\n",
      "\n",
      "(b) Explain why the realized spread profile varies by exchange.\n",
      "\n",
      "(c) Redo the picture adjusting for the following (assumed) take fees:\n",
      "\n",
      "** Exchange ** | ** Take fee ** \n",
      "--- | --- \n",
      "| (**cents**)\n",
      "D | 0.10 \n",
      "B | -0.04\n",
      "Z | 0.29\n",
      "Y | 0.00\n",
      "P | 0.25\n",
      "\n",
      "(d) Based on your results, where would you advise sending a small market order?  How about a large one?\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "rs <- function(lag, ex){\n",
      "    temp <- tqdata[tqdata$EX == ex]\n",
      "    tradeSigns <- getTradeDirection(temp)\n",
      "    p <- as.numeric(temp$PRICE)\n",
      "    n <- length(p)\n",
      "    mids <- (as.numeric(temp$OFR) + as.numeric(temp$BID))/2\n",
      "    rs <- mean(tradeSigns[1:(n-lag)]*(p[1:(n-lag)]-mids[-(1:lag)]))\n",
      "    return (rs)\n",
      "}\n",
      "\n",
      "drawGraph <- function(lag){\n",
      "\n",
      "    rsLagD <- sapply(1:lag, ex = \"D\", rs)\n",
      "    rsLagD\n",
      "    plot(1:lag,rsLagD, col=\"red\",type=\"l\",xlab=expression(tau), ylab = \"Realized spread\", ylim = c(-0.002, 0.006))\n",
      "\n",
      "    rsLagB <- sapply(1:lag, ex = \"B\", rs)\n",
      "    lines(1:lag, rsLagB, col=\"blue\")\n",
      "\n",
      "    rsLagZ <- sapply(1:lag, ex = \"Z\", rs)\n",
      "    lines(1:lag, rsLagZ, col=\"yellow\")\n",
      "\n",
      "    rsLagY <- sapply(1:lag, ex = \"Y\", rs)\n",
      "    lines(1:lag, rsLagY, col=\"green\")\n",
      "\n",
      "    rsLagP <- sapply(1:lag, ex = \"P\", rs)\n",
      "    lines(1:lag, rsLagP, col=\"purple\")\n",
      "\n",
      "    legend(\"topright\", c(\"D...FINRA\", \"B...NASDAQ\", \"Z...BATS Exchange\", \"Y...BATS Y-Exchange\", \"P...NYSE\"), \n",
      "           lty = c(1,1,1,1,1), col=c(\"red\",\"blue\",\"yellow\",\"green\", \"purple\"))    \n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Part (a)\n",
      "lag <- 50\n",
      "drawGraph(lag)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAIAAADytinCAAAgAElEQVR4nOzdd1hT1xsH8G/Clq3I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\nKaBFRCxKAS0iYlH/D24OOASJC/lXAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### (b)\n",
      "\n",
      "Because different exchanges have different processing costs, inventory costs and adverse selection."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Part (C)\n",
      "rs <- function(lag, ex){\n",
      "    temp <- tqdata[tqdata$EX == ex]\n",
      "    tradeSigns <- getTradeDirection(temp)\n",
      "    p <- as.numeric(temp$PRICE)\n",
      "    n <- length(p)\n",
      "    mids <- (as.numeric(temp$OFR) + as.numeric(temp$BID))/2\n",
      "    rs <- mean(tradeSigns[1:(n-lag)]*(p[1:(n-lag)]-mids[-(1:lag)]))\n",
      "    \n",
      "    if(TRUE){\n",
      "        if(ex == \"D\")\n",
      "            rs <- rs + 0.001\n",
      "        else if(ex == \"B\")\n",
      "            rs <- rs - 0.0004\n",
      "        else if(ex == \"Z\")\n",
      "            rs <- rs + 0.0029\n",
      "        else if(ex == \"P\")\n",
      "            rs <- rs + 0.0025        \n",
      "    }\n",
      "\n",
      "    return (rs)\n",
      "}\n",
      "\n",
      "drawGraph <- function(lag){\n",
      "\n",
      "    rsLagD <- sapply(1:lag, ex = \"D\", rs)\n",
      "    rsLagD\n",
      "    plot(1:lag,rsLagD, col=\"red\",type=\"l\",xlab=expression(tau), ylab = \"Realized spread\", ylim = c(-0.002, 0.008))\n",
      "\n",
      "    rsLagB <- sapply(1:lag, ex = \"B\", rs)\n",
      "    lines(1:lag, rsLagB, col=\"blue\")\n",
      "\n",
      "    rsLagZ <- sapply(1:lag, ex = \"Z\", rs)\n",
      "    lines(1:lag, rsLagZ, col=\"yellow\")\n",
      "\n",
      "    rsLagY <- sapply(1:lag, ex = \"Y\", rs)\n",
      "    lines(1:lag, rsLagY, col=\"green\")\n",
      "\n",
      "    rsLagP <- sapply(1:lag, ex = \"P\", rs)\n",
      "    lines(1:lag, rsLagP, col=\"purple\")\n",
      "\n",
      "    legend(\"topright\", c(\"D...FINRA\", \"B...NASDAQ\", \"Z...BATS Exchange\", \"Y...BATS Y-Exchange\", \"P...NYSE\"), \n",
      "           lty = c(1,1,1,1,1), col=c(\"red\",\"blue\",\"yellow\",\"green\", \"purple\"))    \n",
      "}\n",
      "        \n",
      "lag <- 50\n",
      "drawGraph(lag)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAIAAADytinCAAAgAElEQVR4nOzdd1xT1/sH8E8IhBm2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\nRklACyGERv0/dGxVYt6/88QAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### (d)\n",
      "\n",
      "For the small amount market order, choose exchange B for negative fee. For a large amount of the market order, we need to split our order to place."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Predicting trade signs"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 4. (6 points) \n",
      "\n",
      "The following require the *tradeSigns* series from Problem 2.\n",
      "\n",
      "(a) Denote the probability of a sign reversal by $\\pi$.  Derive an expression in terms of $\\pi$ for the conditional expectation $\\E[\\epsilon_t|\\epsilon_{t-1}]$.\n",
      "\n",
      "(b) Assume zero expectation of the trading signs, fit an AR(1) model to the series *tradeSigns*.  What is the coefficient returned by this model?  Explain how  this coefficient relates to $\\pi$?\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### (a)\n",
      "\n",
      "From the definition of expection,\n",
      "$$\n",
      "\\E[\\epsilon_t|\\epsilon_{t-1}] = \\pi(- \\epsilon_{t-1}) + (1 - \\pi) \\epsilon_{t-1}\n",
      "$$\n",
      "\n",
      "So,\n",
      "$$\n",
      "\\pi = \\frac{\\epsilon_{t-1} - \\E[\\epsilon_t|\\epsilon_{t-1}]}{2 \\epsilon_{t-1}}\n",
      "$$\n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (b)\n",
      "AR(1) model\n",
      "$$\\epsilon_t=\\rho\\,\\epsilon_{t-1}+\\eta_t$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# part(b)\n",
      "eplison_t = tradeSigns[-1]\n",
      "eplison_t_minus_one = tradeSigns[-length(tradeSigns)]\n",
      "model1 <- lm(eplison_t ~ 0 + eplison_t_minus_one)\n",
      "rho <- coefficients(model1)\n",
      "cat(\"The rho we fit is\", rho)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "The rho we fit is 0.08472868"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From the AR(1) model, because of independent noise. Then\n",
      "\n",
      "$ \\mathbb{E} [\\epsilon_t|\\epsilon_{t-1}]=\\rho\\,\\epsilon_{t-1}$.\n",
      "\n",
      "From part(a)\n",
      "\n",
      "$ \\mathbb{E} [\\epsilon_t|\\epsilon_{t-1}]= (1 - 2 \\pi) \\epsilon_{t-1}$.\n",
      "\n",
      "So, the relation between them obviously is, \n",
      "\n",
      "$ \\rho = 1 - 2 \\pi $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The MRR model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 5. (6 points)\n",
      "Using the estimate of $\\rho$ (the coefficient obtained from fitting to an AR(1) model) from Problem 4 and equation (11) from the lecture slides:\n",
      "\n",
      "$$\n",
      "\\Delta p_t=(\\phi+\\lambda)\\,\\epsilon_t-(\\phi+\\rho\\,\\lambda)\\,\\epsilon_{t-1}+e_t+\\Delta \\xi_t\n",
      "$$\n",
      "\n",
      "estimate by linear regression the MRR parameters $\\phi$ (transaction cost) and $\\lambda$ (adverse selection or \"Kyle lambda\") from  *tqBAC*.  This amounts to ignoring the autocorrelation of the $\\Delta \\xi_t$.\n",
      "<br>\n",
      "\n",
      "Hint: Use the R function *lm*  to perform the linear regressions."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "p <- as.numeric(tqdata$PRICE)\n",
      "dp <- diff(p)\n",
      "\n",
      "model2 <- lm(dp ~ 0 + eplison_t + eplison_t_minus_one)\n",
      "coeffs <- coefficients(model2)\n",
      "cat(\"The first term coefficient is:\", coeffs[1])\n",
      "cat(\"\\nThe second term coefficient is:\", coeffs[2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "The first term coefficient is: 0.00287475\n",
        "The second term coefficient is: -0.002338937"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Solve the system\n",
      "A <- matrix(data=c(1, 1, -1, -rho), nrow=2, ncol=2, byrow=TRUE)    \n",
      "b <- matrix(data=c(coeffs[1], coeffs[2]), nrow=2, ncol=1, byrow=FALSE)\n",
      "result <- solve(A, b)\n",
      "cat(\"phi is:\", result[1,1])\n",
      "cat(\"\\nlamda is:\", result[2,1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "phi is: 0.002289336\n",
        "lamda is: 0.0005854145"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}